Start advantage in short race: In a 250 m race, A:B speed ratio is 1:2. If A starts 140 m ahead, by how many metres does A win?

Introduction / Context:
Given a significant head start and a speed disadvantage, we compute where A is when B finishes to get A’s winning margin.

Given Data / Assumptions:

• Race length = 250 m
• v_A : v_B = 1 : 2
• A starts at 140 m mark

Concept / Approach:
Time for B to finish = 250/(2u). In that time, A covers additional distance (time * u) beyond the 140 m head start.

Step-by-Step Solution:

Verification / Alternative check:
Proportional scaling confirms A’s progress in half the time B needs (since v_A is half of v_B).

Why Other Options Are Wrong:
They mismatch the precise computation using ratio 1:2 and the given head start.

Common Pitfalls:
Adding/subtracting ratios directly instead of using time comparisons.

Final Answer:
15 m